Method and apparatus for recursively computing equalizer coefficients for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) communications

ABSTRACT

A method of operating a multiple-input multiple-output (MIMO) receiver includes wirelessly receiving a message over a communication channel using a plurality of antennas. The message includes first data preceded by a plurality of training fields. The method includes generating a first matrix indicative of an estimation of properties of the communication channel, and determining a second matrix and a third matrix by performing a matrix decomposition of the first matrix. The method includes, as each of the plurality of training fields of the message is being received, recursively computing parameters for equalization based on (i) the plurality of training fields, (ii) the second matrix, and (iii) the third matrix. The method includes generating equalizer coefficients based on the parameters for equalization, and applying the equalizer coefficients to the first data of the message to compensate the first data.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present disclosure is a continuation of U.S. patent application Ser.No. 12/902,394, filed on Oct. 12, 2010, which is a continuation of U.S.patent application Ser. No. 11/521,182 (now U.S. Pat. No. 7,813,421),filed on Sept. 14, 2006, which claims the benefit of U.S. ProvisionalApplication No. 60/759,453, filed on Jan. 17, 2006. The entiredisclosures of the above referenced applications are incorporated hereinby reference.

FIELD

The present disclosure relates to channel estimation in a wirelesscommunication system.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description which may nototherwise qualify as prior art at the time of filing, are neitherexpressly or impliedly admitted as prior art against the presentdisclosure.

Some multiple input, multiple output (MIMO) wireless communicationsystems can estimate channel conditions, or gains, in the communicationpath between the transmitting and receiving antennas. The channelestimation process can include transmitting known training symbols,receiving the known training symbols, and processing the receivedsymbols to estimate the channel conditions. The estimation is based ondifferences between the known training symbols and the received symbols.Information regarding the channel conditions can then be used to programcoefficients of an equalizer of the receiver. The equalizer thencompensates for the channel conditions.

Referring now to FIG. 1, an example is shown of a MIMO communicationsystem 10 that complies with the Institute of Electrical and ElectronicsEngineers (IEEE) 802.11n specification, which is hereby incorporated byreference in its entirety. A transmitter module 12 communicates with areceiver module 14 via a wireless communication channel 16. A matrix Hrepresents signal gains through channel 16.

Transmitter module 12 periodically generates a plurality of longtraining fields (LTFs) 18-1, . . . , 18-j, referred to collectively asLTFs 18. Each LTF 18 includes a plurality of training symbols 20-1, . .. , 20-k, referred to collectively as training symbols 20. A multipliermodule 22 multiplies each training symbol 20 by a corresponding columnof a preamble steering matrix P. A number of rows n of matrix Pcorresponds with a number of transmit antennas 26-1, . . . , 26-n,collectively referred to as antennas 26. The number of columns j ofmatrix P corresponds with the number of LTFs 18. Matrix P assures theorthogonality of training symbols 20 as they are transmitted fromantennas 26. Matrix P has a condition number of 1, i.e. cond(P) =1.

Receiver module 14 includes receiver antennas 30-1, . . . , 30-n,collectively referred to as antennas 30, that receive the trainingsymbols via channel 16. After receiving all of the training symbols,receiver module 14 generates matrix H based on known training symbols20, matrix P, and the received training symbols. Receiver module 14 canthen use matrix H to adjust coefficients of an internal equalizationmodule for signals from antennas 30. It is generally desirable forreceiver module 14 to generate matrix H as quickly as possible.

A sample estimation of matrix H will now be described. Assume that n=3and j=4. Transmitter module 12 then sends 4 LTFs 18 and matrix P is a3×4 matrix

$P = {\begin{bmatrix}1 & {- 1} & 1 & 1 \\1 & 1 & {- 1} & 1 \\1 & 1 & 1 & {- 1} \\{- 1} & 1 & 1 & 1\end{bmatrix}.}$

The effective MIMO channel estimated at receiver module 14 is given byH_(est)=HP

H=H_(est)P⁻¹, where H_(est) represents an estimation of matrix H. Forthe data associated with each LTF 18 the transmitter-to-receivercommunication model can be described by y=H_(est)P⁻¹x+n, where xrepresents transmitted data symbols. The ZF solution is applied to thematrix H_(est)P⁻¹.

If the matrix P were not used, y=Hx+n

{circumflex over (x)}=R⁻¹Q′y, where y represents received data symbols.With matrix P, y=H_(est)P^(−l)x+n. Receiver module 14 uses each LTF 18to estimate a column of matrix H_(est). Matrix H can therefore beestimated by waiting until all columns have been estimated and thenestimating the matrix_H_(est)P⁻¹. Receiver module 14 can then performorthogonal-triangular decomposition (QR) on H_(est)P⁻¹, i.eQR(H_(est)P⁻¹). However, the computational density increases to theorder of n³, i.e. O(n³). To meet the processing latency the hardwareburden would also increase based on 0(n³).

The effect of matrix P will now be described to shed light on the aboveequations. Let H_(est)=QR. Without matrix P the equalized vector isgiven by

${\hat{x} = {\frac{1}{{diag}\left( {R^{- 1}R^{- *}} \right)}R^{- 1}Q^{*}y}},{{{where}\mspace{14mu} W_{ll}} = {\frac{1}{{diag}\left( {R^{- 1}R^{- *}} \right)}.}}$With matrix P the equalized vector is given by:

${\hat{x} = {\frac{1}{{diag}\left( {\left( {RP}^{- 1} \right)^{- 1}\left( {RP}^{- 1} \right)^{- *}} \right)}{PR}^{- 1}Q^{*}y}},{{{where}\mspace{14mu} W_{ll}} = {\frac{1}{{diag}\left( {\left( {RP}^{- 1} \right)^{- 1}\left( {RP}^{- 1} \right)^{- *}} \right)}.}}$The equivalent matrix RP⁻¹ is a full matrix and it is difficult tocompute its inverse for an n×n communication system.

SUMMARY

A receiver module includes an input that receives a data message from awireless communication channel. The data message has a plurality oftraining fields and data. A channel estimator module recursivelyestimates a matrix H that represents the channel based on the pluralityof training fields. The recursive estimation is performed as theplurality of training fields are being received. An equalizer moduleapplies coefficients to the data based on the matrix H.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating the preferred embodiment of the disclosure, are intended forpurposes of illustration only and are not intended to limit the scope ofthe disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of a multiple input, multipleoutput (MIMO) communication system according to the prior art;

FIG. 2 is a functional block diagram of a MIMO communication system thatincludes a receiver that employs a recursive channel estimation method;

FIG. 3 is a functional block diagram of a MIMO transceiver that includesthe receiver of FIG. 2;

FIG. 4 is a data diagram of a prior art data message that is transmittedby a transmitter module of the communication system of FIG. 2;

FIG. 5 is a flowchart of the recursive channel estimation method;

FIG. 6A is a functional block diagram of a high definition television;

FIG. 6B is a functional block diagram of a vehicle control system;

FIG. 6C is a functional block diagram of a cellular phone;

FIG. 6D is a functional block diagram of a set top box; and

FIG. 6E is a functional block diagram of a media player.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is in no wayintended to limit the disclosure, its application, or uses. For purposesof clarity, the same reference numbers will be used in the drawings toidentify similar elements. As used herein, the term module, circuitand/or device refers to an Application Specific Integrated Circuit(ASIC), an electronic circuit, a processor (shared, dedicated, or group)and memory that execute one or more software or firmware programs, acombinational logic circuit, and/or other suitable components thatprovide the described functionality. As used herein, the phrase at leastone of A, B, and C should be construed to mean a logical (A or B or C),using a non-exclusive logical or. It should be understood that stepswithin a method may be executed in different order without altering theprinciples of the present disclosure.

Referring now to FIG. 2, a functional block diagram is shown of a MIMOcommunication system 50. Communication system 50 includes a receivermodule 52 that employs a recursive channel estimation method (shown inFIG. 5). The recursive channel estimation method estimates conditions ina wireless communication channel 54. The recursive estimation methodbegins with a first long training sequence that is sent by a transmittermodule 56. The recursive estimation method ends by generating a channelestimation matrix H when the last long training sequence has beenreceived. Since the recursive estimation method develops a basis forgenerating matrix H while the long training sequences are beingreceived, instead of starting after the long training sequences havebeen received, the recursive estimation method can generate matrix Hfaster than previously known methods. The matrix H can then be used toperform channel equalization in receiver module 52 to compensate for theeffects of communication channel 54.

Communication system 50 will now be described in pertinent part. Abaseband module 58 generates data messages based on m streams ofincoming data. Baseband module 58 communicates the data messages (shownin FIG. 4) to an encoder module 60. The data messages include respectivelong training fields that are compliant with IEEE 802.11n. Encodermodule 60 encodes the long training fields into n data streams based onthe matrix P, which is shown in FIG. 1. Encoder module 60 communicatesthe n data streams to n respective transmit channels 62-1, . . . , 62-n,which are referred to collectively as transmit channels 62. Eachtransmit channel 62 includes a respective modulation module 64 thatmodulates its respective data stream, such as with quadrature-amplitudemodulation (QAM), and communicates the modulated data stream to arespective inverse fast-Fourier transform (IFFT) module 66. IFFT modules66 convert their respective data streams from a frequency domain signalto a time domain signal. IFFT modules 66 communicate the time domainsignals to respective radio frequency (RF) transmitters that arerepresented by antennas 68.

The transmitted data streams propagate through communication channel 54.Communication channel 54 perturbs the transmitted data streams due tophenomena such as reflections, signal attenuation, and so forth. Theperturbations can be represented by matrix H.

Receiver module 52 includes n RF receivers that are represented byantennas 70-1, . . . , 70-n. The RF receivers receive the transmitteddata streams and communicate the perturbed time domain signals to achannel estimator module 72. Channel estimator module 72 estimatesmatrix H based on matrix P and the long training fields that areincluded in the received data streams. In some embodiments channelestimator module 72 includes a processor 73 and associated memory 75 forstoring and/or executing the recursive channel estimation methods thatare described below.

Channel estimator module 72 communicates the n received data streams ton respective fast-Fourier transform (FFT) modules 74 and adjusts gainsof an equalizer module 76. FFT modules 74 convert the time-domain datastreams to frequency-domain data streams and communicate them toequalizer module 76. Equalizer module 76 compensates the respective datastreams based on the gains and communicates the compensated gains to aViterbi decoder module 78. Viterbi decoder module 78 decodes the n datastreams to generate received data streams y_(m).

Referring now to FIG. 3, a functional block diagram is shown of atransceiver 80 that includes transmitter module 56 and receiver module52. Transceiver 80 can communicate with other transceivers 80 viaantennas 82-1, . . . , 82-n. An antennas switch module 84 selectivelyconnects antennas 82 to transmitter module 56 or receiver module 52based on whether transceiver 80 is transmitting or receiving.

Referring now to FIG. 4, a data diagram is shown of an IEEE 802.11n datamessage 90. Data message 90 includes data 92 and a preamble 94 thatcontains a plurality of training fields. Preamble 94 is divided into afirst portion 96 and a second portion 98. First portion 96 may be usedby legacy systems, e.g. non-MIMO, IEEE 802.11 communication systems.Second portion 98 includes a signal filed field 100, a short trainingfield 102, and x long training fields (LTFs) 104-1, . . . , 104-x, wherex is an integer. Each LTF 104 includes k training symbols 106 or tones.Short training field 102 is generally used by receiver module 52 toestablish symbol timing of data message 90. Channel estimator module 72uses LTFs 104 and their k respective training symbols 106 to estimatematrix H based on methods that are described below.

Referring now to FIG. 5, a method 120 is shown for estimating matrix H.Method 120 can be executed by channel estimator module 72. In someembodiments method 120 can be implemented as a computer program orfirmware that is stored in memory 75 and executed by processor 73.

Control enters at a block 122 and proceeds to decision block 124. Indecision block 124 control determines whether an LTF 104 is beingreceived. If not then control returns to block 122. If an LTF 104 isbeing received then control branches from decision block 124 to block126. In block 126 control receives a training symbol 106 that isassociated with the current LTF 104. Control then proceeds to block 128and updates a matrix H_(est), which is described below in more detail,based on the current training symbol 106. Control then proceeds todecision block 130 and determines whether the current training symbol106 was the last training symbol 106 of the present LTF 104. If not thencontrol branches to block 132 and waits for the next training symbol 106of the current LTF 104. When the next training symbol 106 is receivedcontrol returns to block 126 and repeats the aforementioned steps forthe new training symbol 106. On the other hand, if the training symbol106 in decision block 130 was the last training symbol 106 of thepresent LTF 104 then control branches to decision block 134.

In decision block 134 control determines whether the current LTF 104 wasthe last LTF 104 (i.e. LTF 104-x) of the current group of LTFs 104. Ifnot then control branches to block 136 and waits for the next LTF 104 tobegin before returning to block 126. On the other hand, if the currentLTF 104 was the last LTF 104-x then control branches from decision block134 to block 138. In block 138 control generates matrix H based onmatrix H_(est) and matrix P. Control then proceeds to block 140 andadjusts the gains of equalizer module 76 based on matrix H. Control thenreturns to other processes via termination block 142.

As channel estimator module 72 executes method 120 it performsdistributed QR across LTFs 104. That is, QR(H_(est)). Computationaldensity therefore increases as O(n²) and the processing latency ofassociated hardware and/or processor 73 would increase by about O(n²).This represents an improvement, e.g. reduced need for processing power,over the prior art. Example estimations of matrix H_(est) will now beprovided for various MIMO dimensions of communications system 50.

2×2 and 2×3 MIMO Cases

In 2×2 and 2×3 MIMO cases the equalized vector is given by

$\hat{x} = {\frac{1}{{diag}\left( {P_{2 \times 2}R_{2 \times 2}^{- 1}R_{2 \times 2}^{- *}P_{2 \times 2}^{T}} \right)}P_{2 \times 2}R_{2 \times 2}^{- 1}Q^{*}y}$It can be seen that

$\hat{x} = {\quad{{{{\left\lbrack \begin{matrix}\frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} + r_{12}}}^{2}} & 0 \\0 & \frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} - r_{12}}}^{2}}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}1 & {- 1} \\1 & 1\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}\frac{1}{r_{11}} & {- \frac{r_{12}}{r_{11}r_{22}}} \\0 & \frac{1}{r_{22}}\end{matrix} \right\rbrack} Q^{*} y},\mspace{79mu}{{{where}\mspace{14mu} W_{ll}} = \begin{bmatrix}\frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} + r_{12}}}^{2}} & 0 \\0 & \frac{r_{11}^{2}r_{22}^{2}}{r_{22}^{2} + {{r_{11} - r_{12}}}^{2}}\end{bmatrix}},\mspace{79mu}{P_{2 \times 2} = \begin{bmatrix}1 & {- 1} \\1 & 1\end{bmatrix}},{{{and}\mspace{14mu} R_{2 \times 2}^{- 1}} = {\begin{bmatrix}\frac{1}{r_{11}} & {- \frac{r_{12}}{r_{11}r_{22}}} \\0 & \frac{1}{r_{22}}\end{bmatrix}.}}}}$

4×4 Spatial-multiplexing (SM) MIMO Case

For a general n×n MIMO communication system 50 the equalized vector isgiven by

${\hat{x}}_{n} = {{\frac{1}{{diag}\left( {P_{n}R_{n}^{- 1}R_{n}^{- *}P_{n}^{T}} \right)}P_{n}R_{n}^{- 1}Q_{n}^{*}y\mspace{14mu}{where}\mspace{14mu} H_{{est},n}} = {Q_{n}{R_{n}.}}}$

Methods are known in the art for recursively solving the Q_(n)*y term ofthe above equation. Recursive computation of the P_(n)R_(n) ⁻¹ andw_(ll,n) =1./diag(P_(n)R_(n) ⁻¹R_(n) ⁻*P_(n) ^(T)) terms of the aboveequation will now be described.

4×4 SM MIMO Case—Substream Signal—to Noise Ratio (SNR) Recursion

Let w _(ll,n)=1./diag(P_(n×n)R_(n×n) ⁻¹R_(n×n) ⁻*P_(n×n) ^(T)). It canbe seen that for 1≦j<n the j^(th) element of the w₁₁ vector for nstreams can be recursively computed as follows:

${\frac{1}{w_{{ll},n}^{j}} = {\frac{1}{w_{{ll},{n - 1}}^{j}} + k_{j}}}\mspace{14mu}$${{{where}\mspace{14mu} k_{j}} = \left( {P_{n \times n}{\underset{\_}{vv}}^{*}P_{n \times n}^{T}} \right)_{jj}},{R_{n \times n}^{- 1} = {\left\lbrack {\begin{matrix}R_{n - {1 \times n} - 1}^{- 1} \\\underset{-}{0}\end{matrix}\underset{\_}{v}} \right\rbrack.}}$

${{{For}\mspace{14mu} j} = n},{w_{{ll},n}^{n} = \frac{1}{\lambda_{n} + k_{n}}}$where λ_(n)=P(n,1:n−1)R_(n−1) ⁻¹R_(n−1) ⁻*P(n,1:n−1)^(T).

A proof of the immediately preceding equations will now be provided.

$R_{n \times n}^{- 1} = {{\left\lbrack {\begin{matrix}R_{n - {1 \times n} - 1}^{- 1} \\\underset{-}{0}\end{matrix}\underset{\_}{v}} \right\rbrack{{diag}\left( {P_{n \times n}R_{n \times n}^{- 1}R_{n \times n}^{- *}P_{n \times n}^{T}} \right)}} = {{{diag}\left( {{{P_{n}\left\lbrack {\begin{matrix}R_{n - 1}^{- 1} \\\underset{-}{0}\end{matrix}\underset{\_}{v}} \right\rbrack}\left\lbrack {\begin{matrix}R_{n - 1}^{- 1} \\\underset{-}{0}\end{matrix}\underset{\_}{v}} \right\rbrack}^{*}P_{n}^{T}} \right)} = {{{diag}\left( {{P_{n}\left( {\left\lbrack {\begin{matrix}R_{n - 1}^{- 1} \\\underset{-}{0}\end{matrix}\underset{\_}{0}} \right\rbrack + {\underset{\_}{vv}}^{*}} \right)}P_{n}^{T}} \right)} = {{{diag}\left( {{P_{n - 1}R_{n - 1}^{- 1}R_{n - 1}^{- *}P_{n - 1}^{T}},{P_{({n,{1:{n - 1}}})}R_{n - 1}^{- 1}R_{n - 1}^{- *}P_{({n,{1:{n - 1}}})}^{T}}} \right)} + {{diag}\left( {P_{n}{\underset{\_}{vv}}^{*}P_{n}^{T}} \right)}}}}}$

4×4 SM MIMO Case—Processing the 2^(ND) LTF 104

Compute R_(2×2).

${{Compute}\mspace{14mu} R_{2{\times 2}}^{- 1}} = {\begin{bmatrix}{1/} & {{{- r_{12}}/r_{11}}r_{22}} \\0 & {1/r_{22}}\end{bmatrix}.}$

Compute 1/w_(ll,1)=(r₂₂ ²+∥r₁₁+r₁₂∥²)/r₁₁ ²r₂₂ ².

Compute 1/w_(ll,2)=(r₂₂ ²+∥r₁₁−r₁₂∥²)/r₁₁ ²r₂₂ ².

Let λ=1/w_(ll,2).

4×4 SM MIMO Case—Processing the 3^(RD) LTF 104

Update the inverse of the triangular matrix based on

$R_{3 \times 3} = {{\left\lbrack {\begin{matrix}R_{2 \times 2} \\\underset{-}{0}\end{matrix}\begin{bmatrix}r_{13} & r_{23} & r_{33}\end{bmatrix}}^{T} \right\rbrack R_{3 \times 3}^{- 1}} = \left\lbrack {\begin{matrix}R_{2 \times 2}^{- 1} \\\underset{-}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2} & \rho_{3}\end{bmatrix}}^{T} \right\rbrack}$where  ρ₁ = (r₁₂r₂₃ − r₁₃r₂₂)/r₁₁r₂₂r₃₃ ρ₂ = −r₂₃/r₂₂r₃₃ ρ₃ = 1/r₃₃.

Update the substream SNRs based on1/w _(ll,1)→1/w _(ll,1)+∥ρ₁−ρ₂+ρ₃∥².1/w _(ll,2)→1/w _(ll,2)+∥ρ₁+ρ₂+ρ₃∥².1/w _(ll,3)→λ+∥ρ₁+ρ₂+ρ₃∥².

Update the lamda factor based onλ=1/w _(ll,1)+1/w _(ll,1)−1/w _(ll,3)+8real(ρ₂)ρ₃.

4×4 SM MIMO Case—Processing the 4^(TH) LTF 104

Update the inverse of the triangular matrix based on

$R_{4 \times 4} = {{\left\lbrack {\begin{matrix}R_{3 \times 3} \\\underset{-}{0}\end{matrix}\begin{bmatrix}r_{14} & r_{24} & r_{34} & r_{44}\end{bmatrix}}^{T} \right\rbrack\mspace{14mu} R_{4 \times 4}} = \left\lbrack {\begin{matrix}R_{3 \times 3} \\\underset{-}{0}\end{matrix}\begin{bmatrix}r_{14} & r_{24} & r_{34} & r_{44}\end{bmatrix}}^{T} \right\rbrack}$

whereρ₁=(r ₃₃(r ₁₂ r ₂₄ −r ₁₄ r ₂₂)−(r ₁₂ r ₂₃ −r ₁₃ r ₂₂)r ₃₄)/r ₁₁ r ₂₂ r₃₃ r ₄₄,ρ₂=(r ₃₄ r ₂₃ −r ₂₄ r ₃₃₂)/r ₂₂ r ₃₃ r ₄₄, ρ₃ =−r ₃₃ /r ₃₃ r ₄₄, ρ₄=1/r₄₄.

Update the substream SNR based on1/w _(ll,2)→1/w _(ll,2)+∥ρ₁+ρ₂−ρ₃+ρ₄∥²1/w _(ll,3)→1/w _(ll,3)+∥ρ₁+ρ₂+ρ₃−ρ₄∥²1/w _(ll,4) →λ+∥−ρ ₁+ρ₂+ρ₃+ρ₄∥²1/w _(ll,4) →λ+∥−ρ ₁+ρ₂+ρ₃−ρ₄∥².

Compute their inverses and store them in a memory that can be includedin channel estimator module 72.

3×3 SM MIMO Case—Processing the 4^(TH) LTF 104

The 3×3 MIMO case employs a non-square matrix P. For 3 streamstransmitter module 56 sends 4 LTFs 104 and employs P of P₃

$P_{3} = {\begin{bmatrix}1 & {- 1} & 1 & 1 \\1 & 1 & {- 1} & 1 \\1 & 1 & 1 & {- 1}\end{bmatrix}.}$

Channel estimator module 72 estimates channel matrix H_(est3×4) and thereal matrix is H=H_(est3×4)P_(3×4) ^(⊥). The received vector can bebased on y=H_(est3×4)P_(3×4) ^(⊥)x=Hx.

A distributed solution may also be employed by working directly withH_(est3×4) without forming H. In the distributed solution letH _(est3×4) =QR _(3×4) andH _(est3×4) =[H _(est3×3) h ₄].Then Q*H _(est3×4) =[R Q*h ₄]where QR=H _(est3×3).

In some embodiments the equalized vector can be based on{circumflex over (x)}=(H _(est,3×4) P _(3×4) ^(⊥))^(⊥) y.It can be seen that{circumflex over ( x )}=P ₁ ⁻¹ z −μ v where u =R ⁻¹ Q*h ₄, and μ=[1−1 1]z .The vector v is based onv =kP ₁ ⁻¹ u where u =R ⁻¹ Q*h ₄.The scalar k is based onk=1/(1+[1−1 1] u ).The matrix P₁ ⁻¹ is based on

$P_{1}^{- 1} = {{2\begin{bmatrix}1 & {- 1} & 0 \\1 & 0 & {- 1} \\0 & 1 & 1\end{bmatrix}}.}$

A proof of the immediately preceding equations will now be provided.

A solution is given by {circumflex over (x)}=(H_(est,3×4)P_(3×4)^(⊥))⁻¹y.

Let

$P_{3 \times 4}^{\bot}\begin{bmatrix}P_{1} \\p_{1}\end{bmatrix}$and write the matrix as

$\left( {H_{{est},{3 \times 4}}P_{3 \times 4}^{\bot}} \right)^{- 1} = {\left\lbrack {{H_{{est},{3 \times 3}}P_{1}} + {h_{4}p_{1}}} \right\rbrack^{- 1} = {\left\lbrack {{QRP}_{1} + {h_{4}p_{1}}} \right\rbrack^{- 1} = {{{P_{1}^{- 1}R^{- 1}Q^{*}} - \frac{P_{1}^{- 1}R^{- 1}Q^{*}h_{4}p_{1}P_{1}^{- 1}R^{- 1}Q^{*}}{1 + {p_{1}P_{1}^{- 1}R^{- 1}Q^{*}h_{4}}}} = {\left\lbrack {I - \frac{{vp}_{1}}{1 + {p_{1}v}}} \right\rbrack P_{1}^{- 1}R^{- 1}Q^{*}}}}}$where v=P₁ ⁻¹R⁻¹Q*h₄.

${P_{1}^{- 1} = {2\begin{bmatrix}1 & {- 1} & 0 \\1 & 0 & {- 1} \\0 & 1 & 1\end{bmatrix}}},{{p_{1}P_{1}^{- 1}} = {\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}.}}$

3×3 SM MIMO Case—Solution for W_(ll)

Channel estimator module 72 computesW _(ll)=1/((H _(est,3×4) P _(3×4) ^(⊥))*(H _(est,3×4) P _(3×4) ^(⊥)))⁻¹based on terms of v=kP₁ ⁻¹R⁻¹Q*h₄ and R⁻¹R³¹*.Let this matrix be

${R^{- 1}R^{- *}} = \begin{bmatrix}{I_{11}{jQ}_{11}} & {I_{21}{jQ}_{21}} & {I_{31}{jQ}_{31}} \\{I_{21}{jQ}_{21}} & {I_{22}{jQ}_{22}} & {I_{32}{jQ}_{32}} \\{I_{31}{jQ}_{31}} & {I_{32}{jQ}_{32}} & {I_{33}{jQ}_{33}}\end{bmatrix}$and during LTFs 104 computeS ₁=4(I ₁₁−2I ₂₁ +I ₂₂)S ₂=4(I ₁₁−2I ₃₁ +I ₃₃)S ₃=4(I ₂₂+2I ₃₂ +I ₃₃)S=(I ₁₁ +I ₂₂ +I ₃₃)−2(I ₂₁ +I ₃₃ I ₃₂ )S ₄ =I ₁₁−21I ₂₁ +I ₂₂ −I ₃₁ +I ₃₂ j(Q ₁₁ +Q ₂₂ +Q ₃₁ −Q ₃₂)S ₅ =I ₁₁ −I ₂₁ +I ₃₂ −2I ₃₁ I ₃₃ +j(Q ₁₁ + ₂₁ Q ₃₂ Q ₃₃)S ₆ =I ₂₁ −I ₂₂ +I ₃₁−2I ₃₂ −I ₃₃ +j(Q ₂₁ −Q ₂₂ +Q ₃₁ −Q ₃₃)It can be seen thathd ll1 =1/(S ₁ +S∥v ₁∥²−4real(S ₄ v ₁*))W _(ll2)=1/(S ₂ +S∥V ₂∥²−4real(S ₅ v ₂*))W _(ll3)=1/(S ₃ +S∥v ₃∥²−4real(S ₆ v ₃*))and v=kP₁ ⁻¹ u.

Proof of the above solution for W_(ll) will now be provided. LetH=[QR h ₄ ]P _(3×4) ^(⊥)

Q*H=[R Q*h ₄ ]P _(3×4) ^(⊥)=R(P ₁+ u p ₁), u =R ¹ Q*h ₄

Then

$\left( {H^{*}H} \right)^{- 1} = {{\left( {P_{1} + {\underset{\_}{u}p_{1}}} \right)^{- 1}R^{- 1}{R^{- *}\left( {P_{1}^{T} + {p_{1}^{T}{\underset{\_}{u}}^{*}}} \right)}^{- 1}} = {{\left( {I - \frac{P_{1}^{- 1}\underset{\_}{u}p_{1}}{1 + {\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}\underset{\_}{u}}}} \right)P_{1}^{- 1}R^{- 1}R^{- *}{R_{1}^{- T}\left( {I - \frac{p_{1}^{T}{\underset{\_}{u}}^{*}P_{1}^{- T}}{1 + {\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}\underset{\_}{u}}}} \right)}} = {{\left( {P_{1}^{- 1} - {v\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}}} \right)R^{- 1}{R^{- *}\left( {P_{1}^{- T} - {\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}^{T}v^{*}}} \right)}} = {{P_{1}^{- 1}R^{- 1}R^{- *}P_{1}^{- T}} + {{v\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}}R^{- 1}{R^{- *}\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}}^{T}v^{*}} - {2\;{{real}\left( {P_{1}^{- 1}R^{- 1}{R^{- *}\begin{bmatrix}1 & {- 1} & {- 1}\end{bmatrix}}v^{*}} \right)}}}}}}$v=kP ₁ ⁻¹ R ⁻¹ Q*h ₄.

Channel estimator module 72 still needs to recursively update R⁻¹R⁻*after determining v=kP₁ ⁻¹ u as described above. At a time n letR _(n) ⁻¹ =[R _(n−1) ⁻¹ρ]and apply the following identityR _(n) ⁻¹ R _(n) ⁻ *=R _(n−1) ^(−*)+ρρ*.For example,

$R_{3 \times 3}^{- 1} = \left\lbrack {\begin{matrix}R_{2 \times 2}^{- 1} \\\underset{-}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2} & \rho_{3}\end{bmatrix}}^{T} \right\rbrack$ ρ₁ = (r₁₂r₂₃ − r₁₃r₂₂)/r₁₁r₂₂r₃₃  ρ₂ = −r₂₃/r₂₂r₃₃ ρ₃ = 1/r₃₃.

3×3 SM MIMO Case—Procesing the 1^(ST) LTF 104

Channel estimator module 72 performs first column nulling by computingR ₁ ⁻¹=1/r ₁₁.

3×3 SM MIMO Case—Processing the 2^(ND) LTF 104

Channel estimator module 72 performs second column QR processing basedon

${R_{2 \times 2}^{- 1} = \left\lbrack {\begin{matrix}R_{1}^{- 1} \\\underset{-}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2}\end{bmatrix}}^{T} \right\rbrack}\mspace{14mu}$where  ρ₁ = −r₁₂/r₁₁r₂₂, and  ρ₂ = 1/r₂₂.Channel estimator module 72 then computes ∥ρ₁∥²,∥ρ₂∥², ρ₁ρ₂* and updatesR⁻¹R⁻* based on

${R_{2 \times 2}^{- 1}R_{2 \times 2}^{- *}} = {\begin{bmatrix}{{1/r_{11}} + {\rho_{1}}^{2}} & {\rho_{1}\rho_{2}^{*}} \\{\rho_{1}^{*}\rho_{2}} & {\rho_{2}}^{2}\end{bmatrix}.}$

3−3 SM MIMO Case—Procesing the 3^(RD) LTF 104

Channel estimator module 72 performs third column QR processing byrecursively updating

$R_{3 \times 3}^{- 1} = \left\lbrack {\begin{matrix}R_{2 \times 2}^{- 1} \\\underset{-}{0}\end{matrix}\begin{bmatrix}\rho_{1} & \rho_{2} & \rho_{3}\end{bmatrix}}^{T} \right\rbrack$where ρ₁=(r₁₂r₂₃−r₁₃r₂₂ )/r₁₁r₂₂r₃₃ρ₂=−r₂₃/r₂₂r₃₃ρ₃=1/r₃₃.Channel estimator module 72 can then compute∥ρ₁∥²,∥ρ₂∥²,∥ρ₂∥², ρ₁ρ₂*, ρ₁ρ₃*, ρ_(2ρ) ₃*and update R⁻¹R⁻* based onR _(3×3) ⁻¹ R _(3×3) ⁻ *=R _(2×2) ⁻¹ R _(2×2) ⁻*+ρρ*.

Channel estimator module 72 can then compute the sumsS ₁=4(I ₁₁−2I ₂₁ +I ₂₂)S ₂=4(I ₁₁−2I ₃₁ +I ₃₃)S ₃=4(I ₂₂+2I ₃₂ +I ₃₃)S=(I ₁₁ +I ₂₂ +I ₃₃)−2(I ₂₁ +I ₃₃ I ₃₂ )S ₄ =I ₁₁−2I ₂₁ +I ₂₂ −I ₃₁ +I ₃₂ j(Q ₁₁ +Q ₂₂ +Q ₃₁ −Q ₃₂)S ₅ =I ₁₁ −I ₂₁ +I ₃₂ −2I ₃₁ I ₃₃ +j(Q ₁₁ + ₂₁ Q ₃₂ Q ₃₃)S ₆ =I ₂₁ −I ₂₂ +I ₃₁−2I ₃₂ −I ₃₃ +j(Q ₂₁ −Q ₂₂ +Q ₃₁ −Q ₃₃)

3×3 SM MIMO Case—Procesing the 4^(TH) LTF 104

Channel estimator module 72 computesu =R ⁻¹ Q*h ₄,k=1/(1+[1−1 1] u ), andv =kP ₁ ⁻¹ u .Channel estimator module can store v in memory 75.

Channel estimator module 72 computes substream SNR based onW _(ll1)=1/(S ₁ +S∥v ₁∥²−4real(S ₄ v ₁*))W _(ll2)=1/(S ₂ +S∥v ₂∥²−4real(S ₅ v ₂*))W _(ll3)=1/(S ₃ +S∥v ₃∥²−4real(S ₆ v ₃*))

and store the substream SNR in memory 75.

3×3 SM MIMO Case—Procesing Data 92

Channel estimator module 72 can computez =R ⁻¹ Q*y and μ=[1−1 1] zand read v from memory 75. Channel estimator module 72 can then compute.{circumflex over (x)}=P ₁ ⁻¹ z −μ vand read the substream SNR from memory 75. Equalizer module 76 can scalethe equalized vector based on the SNRs.

Referring now to FIGS. 6A-6E, various exemplary implementations of thereceiver module are shown. Referring now to FIG. 6A, the receiver modulecan be implemented in a high definition television (HDTV) 420. Thereceiver module may implement and/or be implemented in a WLAN interface429. The HDTV 420 receives HDTV input signals in either a wired orwireless format and generates HDTV output signals for a display 426. Insome implementations, signal processing circuit and/or control circuit422 and/or other circuits (not shown) of the HDTV 420 may process data,perform coding and/or encryption, perform calculations, format dataand/or perform any other type of HDTV processing that may be required.

The HDTV 420 may communicate with mass data storage 427 that stores datain a nonvolatile manner such as optical and/or magnetic storage devices.Mass data storage 427 may include at least one hard disk drive (HDD)and/or at least one digital versatile disk (DVD) drive. The HDD may be amini HDD that includes one or more platters having a diameter that issmaller than approximately 1.8″. The HDTV 420 may be connected to memory428 such as RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. The HDTV 420 alsomay support connections with a WLAN via WLAN network interface 429. TheHDTV 420 also includes a power supply 423.

Referring now to FIG. 6B, the receiver module may implement and/or beimplemented in a WLAN interface 448 of a vehicle 430. In someimplementations WLAN interface 448 communicates with a powertraincontrol system 432 that receives inputs from one or more sensors.Examples of sensors includes temperature sensors, pressure sensors,rotational sensors, airflow sensors and/or any other suitable sensorsand/or that generates one or more output control signals such as engineoperating parameters, transmission operating parameters, and/or othercontrol signals.

The receiver module may also be implemented in other control systems 440of the vehicle 430. The control system 440 may likewise receive signalsfrom input sensors 442 and/or output control signals to one or moreoutput devices 444. In some implementations, the control system 440 maybe part of an anti-lock braking system (ABS), a navigation system, atelematics system, a vehicle telematics system, a lane departure system,an adaptive cruise control system, a vehicle entertainment system suchas a stereo, DVD, compact disc and the like. Still other implementationsare contemplated.

The powertrain control system 432 may communicate with mass data storage446 that stores data in a nonvolatile manner. Mass data storage 446 mayinclude at least one HDD and/or at least one DVD drive. The HDD may be amini HDD that includes one or more platters having a diameter that issmaller than approximately 1.8″. The powertrain control system 432 maybe connected to memory 447 such as RAM, ROM, low latency nonvolatilememory such as flash memory and/or other suitable electronic datastorage. The powertrain control system 432 also may support connectionswith a WLAN via a WLAN network interface 448. The control system 440 mayalso include mass data storage, memory and/or a WLAN interface (all notshown). Vehicle 430 may also include a power supply 433.

Referring now to FIG. 6C, the receiver module can be implemented in acellular phone 450 that may include a cellular antenna 451. The receivermodule may implement and/or be implemented in a WLAN interface 468. Insome implementations, the cellular phone 450 includes a microphone 456,an audio output 458 such as a speaker and/or audio output jack, adisplay 460 and/or an input device 462 such as a keypad, pointingdevice, voice actuation and/or other input device. The signal processingand/or control circuits 452 and/or other circuits (not shown) in thecellular phone 450 may process data, perform coding and/or encryption,perform calculations, format data and/or perform other cellular phonefunctions.

The cellular phone 450 may communicate with mass data storage 464 thatstores data in a nonvolatile manner. Mass data storage 450 may includeat least one HDD and/or at least one DVD drive. The HDD may be a miniHDD that includes one or more platters having a diameter that is smallerthan approximately 1.8″. The cellular phone 450 may be connected tomemory 466 such as RAM, ROM, low latency nonvolatile memory such asflash memory and/or other suitable electronic data storage. The cellularphone 450 also may support connections with a WLAN via the WLAN networkinterface 468. The cellular phone 450 may also include a power supply453.

Referring now to FIG. 6D, the receiver module can be implemented in aset top box 480. The receiver module may implement and/or be implementedin a WLAN interface 496. The set top box 480 receives signals from asource such as a broadband source and outputs standard and/or highdefinition audio/video signals suitable for a display 488 such as atelevision and/or monitor and/or other video and/or audio outputdevices. The signal processing and/or control circuits 484 and/or othercircuits (not shown) of the set top box 480 may process data, performcoding and/or encryption, perform calculations, format data and/orperform any other set top box function.

The set top box 480 may communicate with mass data storage 490 thatstores data in a nonvolatile manner. Mass data storage 490 may includeat least one HDD and/or at least one DVD drive. The HDD may be a miniHDD that includes one or more platters having a diameter that is smallerthan approximately 1.8″. The set top box 480 may be connected to memory494 such as RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. The set top box480 also may support connections with a WLAN via the WLAN networkinterface 496. The set top box 480 may include a power supply 483.

Referring now to FIG. 6E, the receiver module can be implemented in amedia player 500. The receiver module may implement and/or beimplemented in a WLAN interface 516. In some implementations, the mediaplayer 500 includes a display 507 and/or a user input 508 such as akeypad, touchpad and the like. In some implementations, the media player500 may employ a graphical user interface (GUI) that typically employsmenus, drop down menus, icons and/or a point-and-click interface via thedisplay 507 and/or user input 508. The media player 500 further includesan audio output 509 such as a speaker and/or audio output jack. Thesignal processing and/or control circuits 504 and/or other circuits (notshown) of the media player 500 may process data, perform coding and/orencryption, perform calculations, format data and/or perform any othermedia player function.

The media player 500 may communicate with mass data storage 510 thatstores data such as compressed audio and/or video content in anonvolatile manner. In some implementations, the compressed audio filesinclude files that are compliant with MP3 format or other suitablecompressed audio and/or video formats. Mass data storage 510 may includeat least one HDD and/or at least one DVD drive. The HDD may be a miniHDD that includes one or more platters having a diameter that is smallerthan approximately 1.8″. The media player 500 may be connected to memory514 such as

RAM, ROM, low latency nonvolatile memory such as flash memory and/orother suitable electronic data storage. The media player 500 also maysupport connections with a WLAN via the WLAN network interface 516. Themedia player 500 may also include a power supply 513. Still otherimplementations in addition to those described above are contemplated.

Those skilled in the art can now appreciate from the foregoingdescription that the broad teachings of the disclosure can beimplemented in a variety of forms. Therefore, while this disclosureincludes particular examples, the true scope of the disclosure shouldnot be so limited since other modifications will become apparent to theskilled practitioner upon a study of the drawings, the specification andthe following claims.

What is claimed is:
 1. A multiple-input multiple-output (MIMO) receivercomprising: a plurality of antennas configured to wirelessly receive amessage over a communication channel, wherein the message includes firstdata preceded by a plurality of training fields; a channel moduleconfigured to generate a first matrix indicative of an estimation ofproperties of the communication channel, determine a second matrix and athird matrix by performing a matrix decomposition of the first matrix,and as each of the plurality of training fields of the message is beingreceived, recursively compute parameters for equalization based on (i)the plurality of training fields, (ii) the second matrix, and (iii) thethird matrix; and an equalizer module configured to generate equalizercoefficients based on the parameters, and apply the equalizercoefficients to the first data of the message to compensate the firstdata, wherein the channel module is configured to recursively computethe parameters for equalization further based on a vector indicative ofa substream signal-to-noise ratio.
 2. The MIMO receiver of claim 1,further comprising a Viterbi decoder module configured to decode thecompensated first data in order to recover user data.
 3. The MIMOreceiver of claim 1, wherein the plurality of training fields have beenpreviously encoded, prior to being transmitted, based on a fourth matrixresponsible for steering the plurality of training fields, and whereinthe equalizer module is configured to: apply the second matrix to avector of the message to generate a first intermediate result; apply thethird matrix to the first intermediate result to generate a secondintermediate result; apply the fourth matrix to the second intermediateresult to generate a third intermediate result; and apply the vector tothe third intermediate result to generate the compensated first data. 4.The MIMO receiver of claim 1, wherein the plurality of training fieldshave been previously encoded, prior to being transmitted, based on afourth matrix responsible for steering the plurality of training fields,and wherein the channel module is configured to recursively compute theparameters for equalization further based on the fourth matrix.
 5. TheMIMO receiver of claim 1, wherein the matrix decomposition of the firstmatrix comprises an orthogonal/upper-triangular (QR) decomposition. 6.The MIMO receiver of claim 5, wherein the second matrix is based on aconjugate transpose of an orthogonal matrix of the QR decomposition, andwherein the third matrix is based on an inverse of an upper triangularmatrix of the QR decomposition.
 7. The MIMO receiver of claim 1, whereinthe channel module is configured to perform one iteration of therecursive computation of the parameters for equalization as each of theplurality of training fields is received.
 8. A transceiver comprising:the MIMO receiver of claim 1; and a MIMO transmitter, wherein the MIMOreceiver and the MIMO transmitter share the plurality of antennas. 9.The transceiver of claim 8, further comprising an antenna switch moduleconfigured to: connect the plurality of antennas to the MIMO receiverwhile the transceiver is receiving, and connect the plurality ofantennas to the MIMO transmitter while the transceiver is transmitting.10. A method of operating a multiple-input multiple-output (MIMO)receiver, the method comprising: wirelessly receiving a message over acommunication channel using a plurality of antennas, wherein the messageincludes first data preceded by a plurality of training fields;generating a first matrix indicative of an estimation of properties ofthe communication channel; determining a second matrix and a thirdmatrix by performing a matrix decomposition of the first matrix; as eachof the plurality of training fields of the message is being received,recursively computing parameters for equalization based on (i) theplurality of training fields, (ii) the second matrix, and (iii) thethird matrix; generating equalizer coefficients based on the parametersfor equalization; and applying the equalizer coefficients to the firstdata of the message to compensate the first data, wherein therecursively computing the parameters for equalization is further basedon a vector indicative of a substream signal-to-noise ratio.
 11. Themethod of claim 10, further comprising decoding the compensated firstdata, using Viterbi decoding, in order to recover user data.
 12. Themethod of claim 10, wherein the plurality of training fields have beenpreviously encoded, prior to being transmitted, based on a fourth matrixresponsible for steering the plurality of training fields, the methodfurther comprising: applying the second matrix to a vector of themessage to generate a first intermediate result; applying the thirdmatrix to the first intermediate result to generate a secondintermediate result; applying the fourth matrix to the secondintermediate result to generate a third intermediate result; andapplying the vector to the third intermediate result to generate thecompensated first data.
 13. The method of claim 10, wherein theplurality of training fields have been previously encoded, prior tobeing transmitted, based on a fourth matrix responsible for steering theplurality of training fields, and wherein the recursively computing theparameters for equalization is further based on the fourth matrix. 14.The method of claim 10, wherein the matrix decomposition of the firstmatrix comprises an orthogonal/upper-triangular (OR) decomposition. 15.The method of claim 14, wherein the second matrix is based on aconjugate transpose of an orthogonal matrix of the QR decomposition, andwherein the third matrix is based on an inverse of an upper triangularmatrix of the OR decomposition.
 16. The method of claim 10, furthercomprising performing one iteration of the recursive computation of theparameters for equalization as each of the plurality of training fieldsis received.